It wasn’t that long ago that any talks leading to a possible major bipartisan deal would include names like former Sens. John Breaux (D-La.) and Sen. Evan Bayh (D-Ind.), former Rep. John Spratt (D-S.C.), Sens. Dick Lugar (R-Ind.) and Olympia Snowe (R-Maine) and, yes, Speaker John Boehner (R-Ohio).

But Breaux, a three-term Senator, retired in 2004, and Bayh, who served two terms as Indiana’s governor and 12 years in the Senate, are now making money, not laws.

In the Senate, Kent Conrad (N.D.), one of the few Democratic Senators truly concerned for years about the deficit, is still around. He is a key figure in the “gang of six,” a mishmash of liberals, conservatives and moderates who are hoping to end the current debt ceiling crisis. But he won’t be around for much longer, as he has chosen not to seek re-election.

Lugar and Snowe are still in the Senate, so they could theoretically play the role of dealmakers. But this year, they are simply out of the mix.

Both are seeking re-election in 2012, with Snowe hoping to avoid a stiff challenge from her political right and Lugar already facing a difficult primary against state Treasurer Richard Mourdock, who has support from the state’s tea party crowd as well as from some local GOP leaders.

On the House side, there are few Democrats still around who have a history of building bridges with the GOP or have built reputations on fiscal responsibility to give them credentials to negotiate with Republicans.

Spratt, who chaired the House Budget Committee for years, was defeated in 2010, and a long list of pragmatic Democrats, from Reps. Walt Minnick (Idaho) and Gene Taylor (Miss.) to Rep. Bart Gordon (Tenn.) either went down to defeat in 2010 or saw the writing on the wall and left of their own volition.

Boehner, of course, is not merely “still around.” He’s the GOP’s leader as Speaker, which theoretically puts him in the position to negotiate a deal.

But, as odd as it may sound, as his party’s leader, Boehner isn’t nearly as free to help broker a compromise as he would be if he were simply an influential senior Member of the party. He’s the leader of an army that is skeptical of its officers, if not downright mutinous. He certainly understands that, and it limits what he can achieve.

There are a few Senators for whom the credential of bridge-builder between the parties should be an asset, including red state Democratic Sens. Ben Nelson (Neb.), Mark Pryor (Ark.), Claire McCaskill (Mo.) and Mary Landrieu (La.), but there are simply too few of them to matter, and not enough of them have earned a widespread reputation for the art of the deal.

Just as important, of course, is that the gulf between the parties has grown wider over the past couple of decades.

Freshman Republican Rep. Nan Hayworth, for example, represents a swing district just north of New York City, and while she is more moderate on social issues such as abortion, she’s a conservative hawk when it comes to tax and deficit issues, reflecting the approach of many of her freshman colleagues from the South and rural Midwest.

During the 1970s and 1980s, liberal Republican Rep. Hamilton Fish Jr. represented most of what is Hayworth’s current district. Moderate Republican Rep. Benjamin Gilman represented the rest of it. It’s unlikely that either man would have been as vociferous as Hayworth about ruling out selective tax increases to cut the deficit and debt, or as eager to cut spending on domestic programs.

There are certainly House Members who would benefit from a satisfactory compromise that shows both parties can be reasonable and principled at the same time.

Purple district Republican Reps. Charles Bass (N.H.), Leonard Lance (N.J.), Dave Reichert (Wash.) and Patrick Meehan (Pa.) surely would be better off with a compromise than without one, as would red district Democratic Reps. Mike McIntyre (N.C.), Jim Matheson (Utah) and Mike Ross (Ark.). But none are in a position to do much, given the nature of the two House caucuses.

The result of all of these changes is that the center — such as it is — can’t force a deal, it can only sit idly by and hope that the left and the right can figure out some sort of arrangement that is satisfactory to each.

That makes the most likely outcome a newer version of “kick the can down the road,” a game that both parties have shown they are very good at.

Voters like the idea of divided government, preferring not to let one party call all the shots. That is understandable, even wise.

But the lack of dealmakers and the growing chasm separating the parties means that divided government is more and more likely to result in paralyzed government than in political compromise, a prospect that voters may find even less appealing.